1.2.3.0 knn_q_from

From a86962cbfd0321387c920a04188512d0de2f3036 Mon Sep 17 00:00:00 2001 From: KatolaZ Date: Mon, 19 Oct 2015 16:30:12 +0100 Subject: First commit of MAMMULT documentation --- doc/html/mammult_docsu34.html | 164 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 164 insertions(+) create mode 100644 doc/html/mammult_docsu34.html (limited to 'doc/html/mammult_docsu34.html') diff --git a/doc/html/mammult_docsu34.html b/doc/html/mammult_docsu34.html new file mode 100644 index 0000000..ccd8b5a --- /dev/null +++ b/doc/html/mammult_docsu34.html @@ -0,0 +1,164 @@ + + +1.2.3.0 knn_q_from_degrees.py + + + + + + + + +

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knn_q_from_degrees.py

NAME +

knn_q_from_degrees.py - compute the inter-layer degree-degree +correlation function. +

SYNOPSYS +

knn_q_from_degrees.py <filein> +

DESCRIPTION +

Compute the inter-layer degree correlation functions for two layers of a +multiplex, using the degrees of the nodes specified in the input file. The format of +the input file is as follows +

ki qi +

where ki and qi are, respectively, the degree at layer 1 and the degree at layer +2 of node i. +

If we consider two layers of a multiplex, and we denote by k the degree +of a node on the first layer and by q the degree of the same node on +the second layers, the inter-layer degree correlation function is defined +as +
+ $k(q) = -1-∑ k′P (k′|q) + Nk ′ + k +$
+

where P(k′|q) is the probability that a node with degree q on the second +layer has degree equal to k′ on the first layer, and N_k is the number of +nodes with degree k on the first layer. The quantity k(q) is the expected +degree at layer 1 of node that have degree equal to q on layer 2. The dual + + + +quantity: +
+ $∑ +q(k) = -1- q′P (q′|k) + Nq q′ +$
+

is the average degree on layer 2 of nodes having degree k on layer +1. +

OUTPUT +

The program prints on stdout a list of lines in the format: +

k q(k) +

where k is the degree on layer 1 and q(k) is the average degree on layer 2 of +nodes having degree equal to k on layer 1. +

The program also prints on stderr a list of lines in the format: +

q k(q) +

where q is the degree on layer 2 and k(q) is the average degree on layer 1 of +nodes having degree equal to q on layer 2. +

REFERENCE +

V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex +networks”, Phys. Rev. E 92, 032805 (2015). +

Link to paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805 +

V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex +networks”, Phys. Rev. Lett. 111, 058701 (2013). +

Link to paper: http://prl.aps.org/abstract/PRL/v111/i5/e058701 +

V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and +condensation in multiplex networks”, Phys. Rev. E 90, 042807 (2014). +

Link to paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807 + + + +

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+ -- cgit v1.2.3